While each child is different and some will not like train travel, the general consensus seems to be that among commercial air, car, and train travel, children do the best with the train.
There are several reasons for this. For one, a train is much more spacious than an airplane or a bus (and certainly more spacious than a car or van). On most long-distance trains, you will find family-friendly movies playing in the evenings. The lower level of the lounge car on Superliner trains (most of the trains outside the east) has tables where board games are frequently played. Children also are quick to make friends with other travelers their age on board.
Another reason children tend to do better on the train is that it is less stressful for everyone. Train connections typically leave more time than air connections – and they don’t happen as often. There is no worrying about maps, finding the next restroom fast, or finding a place to rest overnight. Parents can spend more time with children – and children can amuse themselves more, too.
The dining car offers a special children’s menu at reduced prices. It tends to have items that children will like, such as chicken nuggets or pizza.
In general, children travel at reduced price on Amtrak. Very young children can often travel free.
Amtrak allows carry-on bags and provides many storage spaces for them (more than you’d find on an airplane). As long as you are not excessive with the carry-ons, you should be OK.
Video games, TVs, radios, CD players, etc. may be brought on board, but the sound must be either turned off or headphones must be used to avoid disturbing other passengers. All sleeping car rooms provide low-power AC outlets (more than adequate for most toys and video games). Some coach seats may have them as well.
Infants and Young Children
Children under 2 can often ride free on the train, provided they sit in a parent’s lap (do not consume an extra revenue space).
Restrooms are never far away on Amtrak. Each coach and sleeper car has restrooms. While the restrooms are not spacious, they should provide ample facilities for changing a diaper (many are fitted with changing tables, and the handicap-accessible restrooms provide more room).
If you are traveling in a sleeper on a Superliner train, the Family Bedroom is available to you. It takes up the entire width of one train car, and provides four single-person beds: two adult-size and two child-size. But remember that your children will want to leave the room and explore the train, too.
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Amtrak is the only cross-country passenger railroad in the United States. Outside a few regions, Amtrak is usually the only way to travel state-to-state by rail, and is the only regular option for cross-country travel by rail. Amtrak operates the trains, and mostly runs on tracks owned by freight railroads. Amtrak is a quasi-governmental corporation, created in 1971 when the passenger railroads at the time wanted to get out of the passenger business. For more information on the history of Amtrak, see the Wikipedia article on Amtrak.
Generally, I have found train travel to be competitive with iir, bus, or car travel. Of course, the specifics will vary depending on where you are going, when, and on what train. Check out the How to Travel by Amtrak page for information on getting fares online or by phone. Also, there are lots of discounts available.
This page discusses what you might want to bring with you when you travel on Amtrak.